AP Stats - Chapter 10 Review

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A study of road rage asked separate random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0 to 20. Are the conditions for performing a two-sample t test satisfied?

• Maybe; we have independent random samples, but we need to look at the data to check Normality.
• No; road rage scores in a range between 0 and 20 can’t be Normal.
• No; we don’t know the population standard deviations.
• Yes; we have two independent random samples and large sample sizes.

The power take off drive line on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The drive line is covered by a shield in new tractors, but for a variety of reasons, the shield is often missing on older tractors. Two types of shields are the bolt-on and the flip-up. It was believed that the bolt-on shield was perceived as a nuisance by the operators and deliberately removed, but the flip-up shield is easily lifted for inspection and maintenance and may be left in place. In a study initiated by the U.S. National Safety Council, random samples of older tractors with both types of shields were taken to see what proportion of shields were removed. Of 183 tractors designed to have bolt-on shields, 35 had been removed. Of the 136 tractors with flip-up shields,15 were removed. We wish to perform a test of H0: pb = pf versus Ha: pb > pf, where pb and pf are the proportions of all tractors with the bolt-on and flip-up shields removed, respectively. Which of the following is not a condition for performing the significance test?

• Both populations are Normally distributed.
• The data come from two independent samples.
• Both samples were chosen at random.
• The counts of successes and failures are large enoughto use Normal calculations.

A quiz question gives random samples of n = 10 observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for the difference in the two population means. Janelle uses her calculator’s two-sample t interval with 16.87 degrees of freedom to compute the 95% confidence interval. Assume that both students calculate the intervals correctly.Which of the following is true?

• Tom’s confidence interval is wider.
• Janelle’s confidence interval is wider.
• Both confidence intervals are the same.
• There is insufficient information to determine which confidence interval is wider.

The P-value for the test is 0.048. A correct conclusionis to

• fail to reject H0 at the a = 0.05 level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
• fail to reject H0 at the a = 0.05 level. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
• reject H0 at the a = 0.05 level. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.
• reject H0 at the a = 0.05 level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

At a baseball game, 42 of 65 randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence interval for the difference in population proportions(game − concert) is (−0.154, 0.138). Which of the following gives the correct outcome of the researcher’s test of the claim?

• Because the confidence interval includes 0, the researcher can conclude that the proportion of iPod owners at the two venues is the same.
• Because the center of the interval is –0.008, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.
• Because the confidence interval includes 0, the researcher cannot conclude that the proportion of iPod owners at the two venues is different.
• Because the confidence interval includes more negative than positive values, the researcher can conclude that a higher proportion of people at the rock concert own iPods than at the baseball game.